Hardy Spaces On Homogeneous Groups

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Hardy Spaces On Homogeneous Groups

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Author : Gerald B. Folland
language : en
Publisher: Princeton University Press
Release Date : 2020-12-08

Hardy Spaces On Homogeneous Groups written by Gerald B. Folland and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-12-08 with Mathematics categories.

The object of this monograph is to give an exposition of the real-variable theory of Hardy spaces (HP spaces). This theory has attracted considerable attention in recent years because it led to a better understanding in Rn of such related topics as singular integrals, multiplier operators, maximal functions, and real-variable methods generally. Because of its fruitful development, a systematic exposition of some of the main parts of the theory is now desirable. In addition to this exposition, these notes contain a recasting of the theory in the more general setting where the underlying Rn is replaced by a homogeneous group. The justification for this wider scope comes from two sources: 1) the theory of semi-simple Lie groups and symmetric spaces, where such homogeneous groups arise naturally as "boundaries," and 2) certain classes of non-elliptic differential equations (in particular those connected with several complex variables), where the model cases occur on homogeneous groups. The example which has been most widely studied in recent years is that of the Heisenberg group.

Hardy Spaces On Homogeneous Groups

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Author : Gerald B. Folland
language : en
Publisher: Princeton University Press
Release Date : 1982-06-21

Hardy Spaces On Homogeneous Groups written by Gerald B. Folland and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1982-06-21 with Mathematics categories.

The object of this monograph is to give an exposition of the real-variable theory of Hardy spaces (HP spaces). This theory has attracted considerable attention in recent years because it led to a better understanding in Rn of such related topics as singular integrals, multiplier operators, maximal functions, and real-variable methods generally. Because of its fruitful development, a systematic exposition of some of the main parts of the theory is now desirable. In addition to this exposition, these notes contain a recasting of the theory in the more general setting where the underlying Rn is replaced by a homogeneous group. The justification for this wider scope comes from two sources: 1) the theory of semi-simple Lie groups and symmetric spaces, where such homogeneous groups arise naturally as "boundaries," and 2) certain classes of non-elliptic differential equations (in particular those connected with several complex variables), where the model cases occur on homogeneous groups. The example which has been most widely studied in recent years is that of the Heisenberg group.

Hardy Spaces On Homogeneous Groups

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Author : Gerald B. Folland
language : en
Publisher:
Release Date : 1982

Hardy Spaces On Homogeneous Groups written by Gerald B. Folland and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1982 with categories.

Hardy Inequalities On Homogeneous Groups

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Author : Michael Ruzhansky
language : en
Publisher: Springer
Release Date : 2019-07-02

Hardy Inequalities On Homogeneous Groups written by Michael Ruzhansky and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-07-02 with Mathematics categories.

This open access book provides an extensive treatment of Hardy inequalities and closely related topics from the point of view of Folland and Stein's homogeneous (Lie) groups. The place where Hardy inequalities and homogeneous groups meet is a beautiful area of mathematics with links to many other subjects. While describing the general theory of Hardy, Rellich, Caffarelli-Kohn-Nirenberg, Sobolev, and other inequalities in the setting of general homogeneous groups, the authors pay particular attention to the special class of stratified groups. In this environment, the theory of Hardy inequalities becomes intricately intertwined with the properties of sub-Laplacians and subelliptic partial differential equations. These topics constitute the core of this book and they are complemented by additional, closely related topics such as uncertainty principles, function spaces on homogeneous groups, the potential theory for stratified groups, and the potential theory for general Hörmander's sums of squares and their fundamental solutions. This monograph is the winner of the 2018 Ferran Sunyer i Balaguer Prize, a prestigious award for books of expository nature presenting the latest developments in an active area of research in mathematics. As can be attested as the winner of such an award, it is a vital contribution to literature of analysis not only because it presents a detailed account of the recent developments in the field, but also because the book is accessible to anyone with a basic level of understanding of analysis. Undergraduate and graduate students as well as researchers from any field of mathematical and physical sciences related to analysis involving functional inequalities or analysis of homogeneous groups will find the text beneficial to deepen their understanding.

Anisotropic Hardy Spaces And Wavelets

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Author : Marcin Bownik
language : en
Publisher: American Mathematical Soc.
Release Date : 2003

Anisotropic Hardy Spaces And Wavelets written by Marcin Bownik and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematics categories.

Investigates the anisotropic Hardy spaces associated with very general discrete groups of dilations. This book includes the classical isotropic Hardy space theory of Fefferman and Stein and parabolic Hardy space theory of Calderon and Torchinsky.

Real Variable Theory Of Hardy Spaces Associated With Generalized Herz Spaces Of Rafeiro And Samko

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Author : Yinqin Li
language : en
Publisher: Springer Nature
Release Date : 2023-02-14

Real Variable Theory Of Hardy Spaces Associated With Generalized Herz Spaces Of Rafeiro And Samko written by Yinqin Li and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-02-14 with Mathematics categories.

The real-variable theory of function spaces has always been at the core of harmonic analysis. In particular, the real-variable theory of the Hardy space is a fundamental tool of harmonic analysis, with applications and connections to complex analysis, partial differential equations, and functional analysis. This book is devoted to exploring properties of generalized Herz spaces and establishing a complete real-variable theory of Hardy spaces associated with local and global generalized Herz spaces via a totally fresh perspective. This means that the authors view these generalized Herz spaces as special cases of ball quasi-Banach function spaces. In this book, the authors first give some basic properties of generalized Herz spaces and obtain the boundedness and the compactness characterizations of commutators on them. Then the authors introduce the associated Herz–Hardy spaces, localized Herz–Hardy spaces, and weak Herz–Hardy spaces, and develop a complete real-variable theory of these Herz–Hardy spaces, including their various maximal function, atomic, molecular as well as various Littlewood–Paley function characterizations. As applications, the authors establish the boundedness of some important operators arising from harmonic analysis on these Herz–Hardy spaces. Finally, the inhomogeneous Herz–Hardy spaces and their complete real-variable theory are also investigated. With the fresh perspective and the improved conclusions on the real-variable theory of Hardy spaces associated with ball quasi-Banach function spaces, all the obtained results of this book are new and their related exponents are sharp. This book will be appealing to researchers and graduate students who are interested in function spaces and their applications.

Real Variable Theory Of Musielak Orlicz Hardy Spaces

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Author : Dachun Yang
language : en
Publisher: Springer
Release Date : 2017-05-09

Real Variable Theory Of Musielak Orlicz Hardy Spaces written by Dachun Yang and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-05-09 with Mathematics categories.

The main purpose of this book is to give a detailed and complete survey of recent progress related to the real-variable theory of Musielak–Orlicz Hardy-type function spaces, and to lay the foundations for further applications. The real-variable theory of function spaces has always been at the core of harmonic analysis. Recently, motivated by certain questions in analysis, some more general Musielak–Orlicz Hardy-type function spaces were introduced. These spaces are defined via growth functions which may vary in both the spatial variable and the growth variable. By selecting special growth functions, the resulting spaces may have subtler and finer structures, which are necessary in order to solve various endpoint or sharp problems. This book is written for graduate students and researchers interested in function spaces and, in particular, Hardy-type spaces.

Algebras Of Singular Integral Operators With Kernels Controlled By Multiple Norms

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Author : Alexander Nagel
language : en
Publisher: American Mathematical Soc.
Release Date : 2019-01-08

Algebras Of Singular Integral Operators With Kernels Controlled By Multiple Norms written by Alexander Nagel and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-01-08 with Mathematics categories.

The authors study algebras of singular integral operators on R and nilpotent Lie groups that arise when considering the composition of Calderón-Zygmund operators with different homogeneities, such as operators occuring in sub-elliptic problems and those arising in elliptic problems. These algebras are characterized in a number of different but equivalent ways: in terms of kernel estimates and cancellation conditions, in terms of estimates of the symbol, and in terms of decompositions into dyadic sums of dilates of bump functions. The resulting operators are pseudo-local and bounded on for . . While the usual class of Calderón-Zygmund operators is invariant under a one-parameter family of dilations, the operators studied here fall outside this class, and reflect a multi-parameter structure.

Four Lectures On Real Hp Spaces

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Author : Shanzhen Lu
language : en
Publisher: World Scientific
Release Date : 1995

Four Lectures On Real Hp Spaces written by Shanzhen Lu and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Mathematics categories.

This book introduces the real variable theory of HP spaces briefly and concentrates on its applications to various aspects of analysis fields. It consists of four chapters. Chapter 1 introduces the basic theory of Fefferman-Stein on real HP spaces. Chapter 2 describes the atomic decomposition theory and the molecular decomposition theory of real HP spaces. In addition, the dual spaces of real HP spaces, the interpolation of operators in HP spaces, and the interpolation of HP spaces are also discussed in Chapter 2. The properties of several basic operators in HP spaces are discussed in Chapter 3 in detail. Among them, some basic results are contributed by Chinese mathematicians, such as the decomposition theory of weak HP spaces and its applications to the study on the sharpness of singular integrals, a new method to deal with the elliptic Riesz means in HP spaces, and the transference theorem of HP-multipliers etc. The last chapter is devoted to applications of real HP spaces to approximation theory.

The Mathematical Heritage Of Guido Weiss

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Author : Eugenio Hernández
language : en
Publisher: Springer Nature
Release Date : 2025-01-31

The Mathematical Heritage Of Guido Weiss written by Eugenio Hernández and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-01-31 with Mathematics categories.

This work is a tribute to the life and work of Guido Weiss, a mathematician whose profound contributions shaped the field of harmonic analysis over a span of more than six decades. His groundbreaking research, from pioneering real and complex analysis to his later work on wavelets, continues to influence generations of scholars. More than just a researcher, Guido was a mentor, collaborator, and friend to many, creating a global community of mathematicians. His charisma and generosity fostered lasting professional and personal connections across continents, touching lives far beyond academia. This volume features contributions of collaborators, students, and colleagues of Guido, who had a particularly intense relationship with him. From a heartfelt remembrance of Guido Weiss to advanced discussions on spectral synthesis and wavelet theory, this collection contains a diverse landscape of mathematical results. Readers will delve into topics such as the compactness of bilinear commutators, the intricacies of analytic families in extrapolation theory, and the intersections of time-frequency analysis with modern learning techniques. With contributions to Hardy spaces, Haar multipliers, and crystalline measures, this book serves both as a tribute to past achievements and a beacon for future exploration.